FIG. 1 shows a configuration example of a conventional transmitter in an orthogonal frequency division multiplexing (OFDM) communication system. This transmitter comprises a serial-to-parallel (S/P) converter 101, an inverse fast Fourier transform (IFFT) processor 102 with a size of M, a parallel-to-serial (P/S) converter 103, a limiter 104, low pass filters (LPFs) 105 and 107, a digital-to-analog converter (DAC) 106, a radio frequency (RF) up-converter 108 and a high-power amplifier (HPA) 109 operating in class A or A-B.
The S/P converter 101 converts the input bit stream 111 representing data to be transmitted into parallel signals. The IFFT processor 102 operates as an interpolator and performs M×K IFFT over the parallel signals with an oversampling factor of K. The P/S converter 103 converts output signals from the IFFT processor 102 into a signal S(t).
The amplitude of the signal S(t) is clipped at the level A by the limiter 104. Such clipping is implemented for reducing peak-to-average power ratio (PAPR) of OFDM signals, i.e. removing the high amplitude peak. In order to avoid growth of the out-of-band radiation, however, an additional LPF 105 is necessary. The output signal from the limiter 104 passes through the LPF 105 for out-of-band power suppression and the filtered signal is output to the DAC 106 and limiter 104.
The DAC 106 converts an output signal S*(t) from the LPF 105 into an analog signal. The output analog signal passes through the LPF 107 and up-converted by the RF up-converter 108. The HPA 109 amplifies the obtained RF signal and outputs it to an antenna (not shown).
The filter task is based upon a finite-impulse response (FIR) with N coefficients and recursive filters. The direct form realization of the FIR is the convolutional summation such as the following equation (see non-patent document 1).
                              y          ⁡                      (            n            )                          =                              ∑                          k              =              0                                      N              -              1                                ⁢                                    h              ⁡                              (                k                )                                      ·                          x              ⁡                              (                                  n                  -                  k                                )                                                                        (        1        )            
In equation (1), y(n) is an FIR output signal, x(n) is an FIR input signal, h(n) is unit samples of the FIR and N is the length of the FIR (number of the filter taps). In the case of the configuration shown in FIG. 1, it is assumed that S*(t)=y(n).
The structure of an FIR filter based on equation (1) is shown in FIG. 2. The FIR filter comprises delays 201-1 through 202-(N−1), multipliers 202-0 through 202-(N−1) and adders 203-1 through 203-(N−1). As can be seen from FIG. 2, the number of multiplication operations for the FIR with N taps equals N.
For example, in an OFDM communication system with a large number of subcarriers, in order to obtain the strong out-of-band power suppressions (typically −50 through −75 dB), an LPF must have very long pulse response. This causes a very large number of multiplications during filtration and the total number of FIR's weight coefficients must be large. According to simulation results described later, an FIR with at least 512 taps can provide the necessary out-of-band power suppressions.
In application specific integrated circuit (ASIC) or field programmable gate array (FPGA) implementations, an 8-bit multiplier is about 8 times more complex than an adder. Thus, a reduction of the number of multipliers is the primary target for the complexity reduction in a digital filter device.
In a prior Japan patent application No. 2006-324736, it was shown that a clipping-and-filtering approach employed the LPF 105 shown in FIG. 1 can be represented as shown in FIG. 3 with replacement of the LPF 105 with a high pass filter (HPF) 302. The operation of a constituent element shown in FIG. 3 with the same numeral as that of a constituent element shown in FIG. 1 is similar to the operation of the element.
A limiter 301 clips the amplitude of the signal S(t) and outputs a clipping signal Clip (t) and a clipped signal S*(t) (=S(t)−Clip (t)). The HPF 302 is configured as shown in FIG. 2 and controlled by a controller 303 to perform a high pass filtering of the clipping signal Clip (t). The controller 303 receives the clipping signal Clip (t) from the HPF 302 and enables the HPF 302 to skip multiplication operations for zero-value samples included in the clipping signal Clip (t). An adder 304 adds the filtered signal and the clipped signal S*(t) and outputs a resulting signal to the DAC 106 and the limiter 301.
An out-of-band component of the clipping signal Clip (t) output from the HPF 302 is in opposite phase to that of the out-of-band component of the clipped signal S*(t). Therefore, adding the output signal and the clipped signal S*(t), the out-of-band component of the clipped signal S*(t) is cancelled out.
As described above, the clipped signal or the clipping signal is filtered in the LPF 105 shown in FIG. 1 or the HPF 302 shown in FIG. 2 to remove the resulting out-of-band power. In Non-patent Documents 2 and 3, the LPF filter unit is composed of a pair of larger FFT and IFFT modules. In Non-patent Document 4, the filter task is based upon an FIR with 103 coefficient and recursive filters.
For example, FIG. 4 shows simulation results of the level of out-of-band power suppression for a world wide interoperability for microwave access (WiMAX) system with 2048 subcarriers. ATT expressed in dB represents the level of out-of-band power suppression, the clipping level or clipping ratio (CR) equals 4 dB and the number of FIR's taps N is used as a parameter. A curved line 401 represents an OFDM signal spectrum after clipped at the level of 4 dB and three curved lines 406 represent a theoretical OFDM signal spectrum, an OFDM signal spectrum without clipping and an OFDM signal spectrum after clipped at the level of 4 dB and filtered by an LPF, where the three overlap each other. Four curved lines 402, 403, 404 and 405 represent signal spectra of FIRs with 64, 128, 256 and 512 taps, respectively.
Plots in FIG. 4 show the substantial improvement in the out-of-band power suppression when the length of FIR (the number of taps N) increases. Thus, according to the simulation results, the FIR with 512 taps provides satisfactory out-of-band power suppressions. Obviously, the FIRs with less than 512 taps provide unsatisfactory out-of-band power suppression. a Larger number of taps requires a larger number of multipliers that are more complex than adders.
Let's consider the special type of the input signal x(t). It is supposed that the input signal x(t) contains several samples with zero amplitude. A good example of such a zero-containing signal is the clipping signal Clip (t). According to the configuration shown in FIG. 3, the clipping signal Clip (t) can be described by the following equations.
                              S          ⁡                      (            t            )                          =                  ρ          ·                      exp            ⁡                          (                              j                ·                φ                            )                                                          (        2        )                                                      S            *                    ⁡                      (            t            )                          =                  {                                                                      S                  ⁡                                      (                    t                    )                                                                                                                    for                    ⁢                                                                                  ⁢                    ρ                                    <                  A                                                                                                      A                  ·                                      exp                    ⁡                                          (                                              j                        ·                        φ                                            )                                                                                                                                        for                    ⁢                                                                                  ⁢                    ρ                                    >                  A                                                                                        (        3        )                                          Clip          ⁢                                          ⁢                      (            t            )                          =                              S            ⁡                          (              t              )                                -                                    S              *                        ⁡                          (              t              )                                                          (        4        )            
In equations (2) and (3), S(t) is the original (non-clipped) OFDM signal and S*(t) is the clipped signal. Further, ρ and φ are an amplitude and a phase, respectively, of S(t) and A is the clipping level or CR. Clip (t) in equation (4) represents the difference between the original signal S(t) and the clipped signal S*(t).
According to equation (4), the clipping signal Clip (t) has non-zero values only in the case when the original signal S(t) exceeds the CR. Thus, according to an OFDM complementary cumulative distribution function (CCDF), for most practical CR values (3 through 6 dB), the probabilities exceeding peak-to-average power ratio (PAPR) level are relatively low. Therefore, the clipping signal Clip (t) contains mostly zero samples together with a few non-zero samples (see FIG. 5). In FIG. 5, the clipping signal Clip (t) contains 84%, 90%, 95% and 97.2% of zero samples for CR values of 3, 4, 5 and 6 dB, respectively.
Thus, it is obvious that multiplications with the following additions can be omitted during implementation filtering shown in FIG. 2 (equation (1)) for all zero-value samples x(t). Despite operation reduction in this case, however, the total amount of hardware (the number of multipliers and adders) in the FIR shown in FIG. 2 cannot be reduced. It is not possible to simply remove some multipliers and adders because they might be required to process another non-zero samples at the next FIR cycle.
Patent Document 1 relates to an FIR filter where increase of the number of necessary multiplier circuits is prevented.    Patent Document 1: Japanese Patent Application Publication No. 2002-158561    Non-patent Document 1: J. G. Proakis and D. G. Manolakis, “Digital Signal Processing; Principle, Algorithms, and Applications,” Prentice Hall, p. 503, 1996.    Non-patent Document 2: J. Armstrong, “New OFDM Peak-to-Average Power Reduction Scheme,” Proceedings of VTC, vol. 1, pp. 756-760, May 2001.    Non-patent Document 3: H. A. Suraweera, K. R. Panta, M. Feramez and J. Armstrong, “OFDM Peak-to-Average Power Reduction Scheme with Spectral Masking,” Proceedings of International Symposium on Communication Systems Networks and Digital Signal Processing (CSNDSP 2004), pp. 160-163, July 2004.    Non-patent Document 4: L. D. Kabulepa, T. Pionteck, A. Garcia and M. Glesner, “Design Space Exploration for Clipping and Filtering PAPR Reduction Techniques in OFDM Systems,” Proceedings of the 8th International OFDM Workshop, pp. 108-112, 2003.